Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two ... [more ▼]

Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-Z and controlled-NOT gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-NOT gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided. [less ▲]

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K < 2, through large scale numerical simulations and finite-size scaling analysis. We find that ... [more ▼]

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K < 2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In the critical regime, multifractal wave functions are located on a few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results. [less ▲]

Arrays of qubits encoded in the ground state manifold of trapped neutral atoms appear as a promising platform for the realisation of a scalable quantum computer. Indeed, such physical qubits have a long ... [more ▼]

Arrays of qubits encoded in the ground state manifold of trapped neutral atoms appear as a promising platform for the realisation of a scalable quantum computer. Indeed, such physical qubits have a long coherence time and allow for high-fidelity single-qubit operations [1]. In such a platform, entangling two-qubit gates can be implemented by exploiting the Rydberg-blockade mechanism to produce a phase shift or a flip of the state of a target atom conditioned on the state of a control atom [2]. However, because dipole-dipole interactions fall off rapidly with the interatomic distance, such entangling gates based on Rydberg-blockade are impractical between distant qubits. In this work, we propose a protocol to implement long-range Rydberg-blockade gates (CZ or CNot) using auxillary non-coding atoms to transfer the Rydberg excitation from the control to the target qubit. The dependence of the fidelity on the number of auxillary atoms, the blockade strength and the decay rates of the Rydberg states are determined. When compared to a sequential application of nearest neighbours entangling gates, our protocol leads to a larger fidelity and a reduction of the overall gate duration (which scales linearly with the number of auxillary atoms). [1] M. Saffman, J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016). [2] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Phys. Rev. Lett. 85, 2208 (2000). [less ▲]

Among all possible spin states, spin-coherent states are the most classical because the spin expectation value in these states yields a vector of maximal norm pointing in a well defined direction. In ... [more ▼]

Among all possible spin states, spin-coherent states are the most classical because the spin expectation value in these states yields a vector of maximal norm pointing in a well defined direction. In contrast, anticoherent spin state to order t are such that <(J.n)^k> is independent of the unit vector n for k = 1, ..., t [1]. By construction, coherent and anticoherent spin states are at both ends of the spectrum of classicality. The aim of this work is to position all possible spin states on such a spectrum, that is to provide measures of anticoherence. To this aim, we introduce an axiomatic definition of anticoherence measures to any order t. In particular, we show that the total variance of a pure spin state, first introduced in [2] can be used to define a measure of anticoherence to order 1. We describe a systematic way of constructing anticoherence measures to any order that relies on the mapping between spin-j states and symmetric states of N = 2j spin-1/2. In particular, we exploit the fact that anticoherent spin states to order t have maximally mixed t-spin-1/2 reduced density matrices in the symmetric subspace [3]. [1] J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006). [2] A. A. Klyachko, B. Öztop, and A. S. Shumovsky, Phys. Rev. A 75, 032315 (2007). [3] D. Baguette, T. Bastin, and J. Martin, Phys. Rev A 90, 032314 (2014). [less ▲]

In this paper, we study the competition between finite-size effects (i.e. discernibility of particles) and dipole–dipole interactions in few-atom systems coupled to the electromagnetic field in vacuum. We ... [more ▼]

In this paper, we study the competition between finite-size effects (i.e. discernibility of particles) and dipole–dipole interactions in few-atom systems coupled to the electromagnetic field in vacuum. We consider two hallmarks of cooperative effects, superradiance and subradiance, and compute for each the rate of energy radiated by the atoms and the coherence of the atomic state during the time evolution. We adopt a statistical approach in order to extract the typical behaviour of the atomic dynamics and average over random atomic distributions in spherical containers with prescribed k0 R with k0 the radiation wavenumber and R the average interatomic distance. Our approach allows us to highlight the tradeoff between finite-size effects and dipole– dipole interactions in superradiance/subradiance. In particular, we show the existence of an optimal value of k0R for which the superradiant intensity and coherence pulses are the less affected by dephasing effects induced by dipole–dipole interactions and finite-size effects. [less ▲]

In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the ... [more ▼]

In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the possibility of chaos in the case of stationary nodes. We address this question by considering stationary states, which provide the simplest examples of wave functions with stationary nodes. We provide examples of stationary wave functions for which there is chaos, as demonstrated by numerical computations, for one particle moving in 3 spatial dimensions and for two and three entangled particles in two dimensions. Our conclusion is that the motion of the nodes is not necessary for the generation of chaos. What is important is the overall complexity of the wave function. That is, if the wave function, or rather its phase, has complex spatial variations, it will lead to complex Bohmian trajectories and hence to chaos. Another aspect of our work concerns the average Lyapunov exponent, which quantifies the overall amount of chaos. Since it is very hard to evaluate the average Lyapunov exponent analytically, which is often computed numerically, it is useful to have simple quantities that agree well with the average Lyapunov exponent. We investigate possible correlations with quantities such as the participation ratio and different measures of entanglement, for different systems and different families of stationary wave functions. We find that these quantities often tend to correlate to the amount of chaos. However, the correlation is not perfect, because, in particular, these measures do not depend on the form of the basis states used to expand the wave function, while the amount of chaos does. [less ▲]

We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of ... [more ▼]

We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates γ and γ0 and a single parameter dd describing the dipole-dipole shifts. We solve the dynamics exactly for N = 2 atoms, numerically for up to 30 atoms, and obtain the large-N limit by a mean-field approach. We find that there is a critical difference γ0 − γ that depends on N beyond which superradiance is lost. We show that exact nontrivial dark states (i.e., states other than the ground state with vanishing spontaneous emission) only exist for γ = γ0 and that those states (dark when γ = γ0) are subradiant when γ < γ0. [less ▲]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion [1]. Our equation provides a unifying ... [more ▼]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion [1]. Our equation provides a unifying picture of the consequences of recoil and in- distinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and is relevant for experiments with ultracold trapped atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find analytical formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that the dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. The effects predicted should be experimen- tally observable with Rydberg atoms [2]. [1] F. Damanet, D. Braun, and J. Martin, arXiv:1512.06676v2. [2] K. Afrousheh, P. Bohlouli-Zanjani, D. Vagale, A. Mugford, M. Fedorov, and J. D. D. Martin, Phys. Rev. Lett. 93, 233001 (2004) [less ▲]

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical ... [more ▼]

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical computations, for one particle moving in 3 spatial dimensions and for two and three entangled particles in 2 dimensions. What is important for the amount of chaos is the overall complexity of the wave function. Some simple measures that partly capture the complexity of the wave function are considered: the participation ratio and different measures of entanglement. We find that these measures often tend to correlate to the amount of chaos. However, the correlation is not perfect, because the measures do not depend on the intrinsic complexity of the states of a given basis. [less ▲]

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created ... [more ▼]

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by {\it Couder et al} [Phys. Rev. Lett. {\bf 97}, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics. [less ▲]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including the quantization of their motion. Our equation provides a unifying picture of the effects of ... [more ▼]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including the quantization of their motion. Our equation provides a unifying picture of the effects of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, generalizing those in Ref. [1]. We find closed-form formulas for a number of relevant states (gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission [2] can be modulated through the external state of motion. As an application of our general formalism, we study the spatial Pauli blocking of two fermionic atoms beyond the Lamb-Dicke regime [3]. [1] G. S. Agarwal, Springer Tracts In Modern Physics 70, 1 (1974). [2] R. H. Dicke, Phys. Rev. 93, 99 (1954). [3] R. M. Sandner, M. Müller, A. J. Daley & P. Zoller, Phys. Rev. A 84, 043825 (2011). [less ▲]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana ... [more ▼]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana represen- tation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state [1]. We focus on the identi cation of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three di erent characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then in- vestigate in detail the case of small numbers of qubits and construct in nite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order. [1] D. Baguette et al., Phys. Rev. A 92, 052333 (2015). [less ▲]

We investigate multiqubit permutation-symmetric states with maxi- mally mixed reduced density matrices in the symmetric subspace [1]. Such states can be viewed as particular spin states, namely anticoher ... [more ▼]

We investigate multiqubit permutation-symmetric states with maxi- mally mixed reduced density matrices in the symmetric subspace [1]. Such states can be viewed as particular spin states, namely anticoher- ent spin states [2]. Using the Majorana representation of spin states in terms of points on the unit sphere [3], we analyze the consequences of degeneracies of the Majorana points and of a point-group symmetry in their arrangement on the existence of anticoherent spin states. We provide different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and SLOCC classes [4]. We consider in detail the case of small numbers of qubits and solve the 4-qubit case completely by identifying and characterizing all 4-qubit anticoherent states. [1] D. Baguette, T. Bastin, and J. Martin, Phys. Rev. A 90, 032314 (2014); O. Giraud et al., Phys. Rev. Lett. 114, 080401 (2015); D. Baguette et al., Phys. Rev. A 92, 052333 (2015). [2] J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006). [3] E. Majorana, Nuovo Cimento 9, 43 (1932). [4] SLOCC classes : Classes of states equivalent through stochastic local operations with classical communication. [less ▲]

We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying ... [more ▼]

We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states, and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. [less ▲]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana ... [more ▼]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then investigate in detail the case of small numbers of qubits and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order. [less ▲]

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a ... [more ▼]

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong-enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems. [less ▲]

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the ... [more ▼]

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the guiding equation. This equation states that the velocity of the particle is proportional to the usual probability current associated with its wave function. In this work, we study the quantum trajectory of a single particle in a Coulomb potential whose eigenstates are the well known eigenstates of the hydrogen atom. More precisely, we focus on the relation between chaotic Bohmian trajectories and the motion of wave function nodes. At wave function nodes i.e., where the wave function vanishes, the velocity is not defined which generically induces vorticity. In order to probe chaos, we compute Poincaré map and we numerically evaluate Lyapounov exponents, which characterize the divergence of close trajectories as time increases. For the 2d Coulomb potential, although the superposition of two eigenstates with different energies can lead to an arbitrary high number of moving nodes of the wave function, the Bohmian trajectories display no trace of chaos. This absence of chaotic behaviour originates from the existence of a constant of motion. Therefore, the motion and the number of nodes do not constitute a sufficient condition for the emergence of chaos in Bohmian mechanics. For superpositions of more than two eigenstates, there is no constant of motion, there are moving nodes and we find that the Bohmian trajectories are chaotic. [less ▲]